Question

(a) What do you mean by the $Q$ value of nuclear reaction?
(b) Write down the expression for $Q$ value in the class of $\alpha $ decay.

Answer 1

Hint: Nuclear reaction is a process in which two nudei or nuclear particles collide, to produce different products than initial particles. In principle a reaction can involve more than two particles. Colliding but such an event is exceptionally rare.
Formula:-
It is determined from the masses of reactants and product $Q$ value affects reaction routes.
In general, the larger the positive $Q$ values for the reaction the faster the reaction proceeds. And the more likely the reaction.
$Q=\left( {{m}_{r}}-{{m}_{p}} \right).931MeV$
Where ${{M}_{r}}\And {{M}_{P}}$ are the sum of the reactant and product masses.

Complete step by step solution:
(a) In nuclear physics and chemistry, the $Q$ value for a reaction is the amount of energy absorbed or reaction during the nuclear reaction. The value relates enthalpy of a chemical reaction or the energy of radioactive decay products.
The $Q$ value of the reaction is defined as the difference between the sum of the masses of the initial reactants and the sum of the masses of the final product in energy units (usually in $MeV)$ It is the measure of amount of energy released by the reaction.
(b) The $Q-$Value of the decay, ${{Q}_{a}}$ is the difference of the mass of the parent $({{M}_{p}})$ and the combined mass of the daughter $(({{M}_{P}}$ and $\alpha -$particle $\left( {{M}_{a}} \right))$ multiplied by ${{c}^{2}}:$
${{Q}_{a}}=\left( {{M}_{P}}-{{M}_{0}}-{{M}_{a}} \right){{c}^{2}}$

Additional information:
A typical nuclear reaction involves two reacting particles, a heavy target nucleus and a light bombarding particle and produces two new particles. A heavier product nucleus and a lighter ejected particle.

Note:
In this question the value $Q$ is difference between the sum of the mass of the initial reactions and final product-mass and the equation of ${{Q}_{a}}$ is $\left( {{M}_{P}}-{{M}_{0}}-{{M}_{a}} \right){{c}^{2}}$